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7997 results in Fluid dynamics and solid mechanics

Page 351 of 400

  • 7 - Wall flows

  • from PART ONE - FUNDAMENTALS
  • Stephen B. Pope, Cornell University, New York
  • Book:
    Turbulent Flows
    Published online:
    05 June 2012
    Print publication:
    10 August 2000, pp 264-332

  • Summary

    In contrast to the free shear flows considered in Chapter 5, most turbulent flows are bounded (at least in part) by one or more solid surfaces. Examples include internal flows such as the flow through pipes and ducts; external flows such as the flow around aircraft and ships' hulls; and flows in the environment such as the atmospheric boundary layer, and the flow of rivers.

    We consider three of the simplest of these flows (sketched in Fig. 7.1), namely: fully developed channel flow; fully developed pipe flow; and the flat-plate boundary layer. In each of these flows the mean velocity vector is (or is nearly) parallel to the wall, and, as we shall see, the near-wall behaviors in each of these cases are very similar. These simple flows are of practical importance and played a prominent role in the historical development of the study of turbulent flows.

    Central issues are the forms of the mean velocity profiles, and the friction laws, which describe the shear stress exerted by the fluid on the wall. In addition the mixing length is introduced in Section 7.1.7; the balance equations for the Reynolds stresses are derived and examined in Section 7.3.5; and the proper orthogonal decomposition (POD) is described in Section 7.4.

    Channel flow

    A description of the flow

    As sketched in Fig. 7.1, we consider the flow through a rectangular duct of height h = 2δ. The duct is long (L/δ ≫ 1) and has a large aspect ratio (b/δ ≫ 1).

Page 351 of 400